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Assertion : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$
Reason : The permissible error is calculated by the formula $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$
Students $A, B$ and $C$ measure the length of a room using $25 \,m$ long measuring tape of least count $0.5 \,cm$, meter-scale of least count $0.1 \,cm$ and a foot-scale of least count $0.05 \,cm$, respectively. If the specified length of the room is $9.5 \,m$, then which of the following students will report the lowest relative error in the measured length?
In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are $50$ divisions on the circular scale, and the main scale moves by $0.5 \,{mm}$ on a complete rotation. For a particular observation the reading on the main scale is $5\, {mm}$ and the $20^{\text {th }}$ division of the circular scale coincides with reference line. Calculate the true reading. (in ${mm}$)
The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $\mathrm{h} / \sqrt{2 m E}$ The dimensional formula for Planck's constant is:
The length, breadth and thickness of a block are given by $l = 12\,cm,\,b = 6\,cm$ and $t = 2.45\,cm$ The volume of the block according to the idea of significant figures should be